Finite Group Databasebeta

← C2×#20286919 #28260892

Subgroups — C2×#20286919 #28260892

Order 13568.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811321C211yesmaximal, characteristic, complemented
2C2×#16811270C211yesmaximal, characteristic, complemented
3#20286919C2116yesmaximal, direct product factor
4C2×#16810976C211yesmaximal, characteristic, complemented
5C2×#16810966C211yesmaximal, characteristic, complemented
6C2×#16810926C211yesmaximal, characteristic, complemented
7C2×#16810874C211yesmaximal, characteristic, complemented
8C2×#16810870C211yesmaximal, characteristic, complemented
9C2×#16810837C211yesmaximal, characteristic, complemented
10C2×#16810770C211yesmaximal, characteristic, complemented
11C2×#16810758C211yesmaximal, characteristic, complemented
12C2×#16810705C211yesmaximal, characteristic, complemented
13C2×#16810698C211yesmaximal, characteristic, complemented
14C2×#16810622C211yesmaximal, characteristic, complemented
15C2×#16810626C211yesmaximal, characteristic, complemented
16C2×C53×#480C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719913C2211yescharacteristic, complemented
20C22×D424C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22C22×#11719917C2211yescharacteristic, complemented
23C22×#11719912C2211yescharacteristic
24#16811321—24no—
25#16811321C2218yescomplemented
26#16811270—24no—
27#16811270C2218yescomplemented
28C2×#13133212—21no—
29C2×#13133208C2211yescharacteristic, complemented
30C2×#13133204C2211yescharacteristic
31C2×#13133202—21no—
32C2×#13133199—21no—
33C2×#13133197C2211yescharacteristic
34C2×#13133192C2211yescharacteristic
35C2×#13133191—21no—
36C2×#13133191C2211yescharacteristic, complemented
37C2×#13133188—21no—
38C2×#13133185—21no—
39C2×#13133179C2211yescharacteristic
40C2×#13133179C2211yescharacteristic, complemented
41C2×C4×C22⋊D53—21no—
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×#13133175C2211yescharacteristic
44C2×C22⋊C4×D53—21no—
45#16810976C2218yescomplemented
46#16810966C2218yescomplemented
47#16810926C2218yescomplemented
48#16810874C2218yescomplemented
49#16810870C2218yescomplemented
50#16810837C2218yescomplemented
51#16810770C2218yescomplemented
52#16810758C2218yescomplemented
53#16810705C2218yescomplemented
54#16810698C2218yescomplemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×#13133146C2211yescharacteristic, complemented
57#16810626C2218yescomplemented
58#16810622C2218yescomplemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133140C2211yescharacteristic, complemented
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic, complemented
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic, complemented
69C2×#121×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic, complemented
71C53×#480C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#107×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719945—22no—
79C2×#11719945—24no—
80C2×#11719945—42no—
81C2×#11719945C2314yes—
82C22×Dic106C2311yescharacteristic
83C22×D212—21no—
84C22×D212C2311yescharacteristic
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53D411yescharacteristic
90C2×D4×D53—24no—
91C2×D4×D53—22no—
92C2×D4×D53—42no—
93C2×D4×D53C2314yes—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53—21no—
97C22×C4×D53C2311yescharacteristic
98C2×#11719913—42no—
99C2×#11719913C2314yescomplemented
100C2×D424—24no—
101C2×D424C2314yes—
102C2×#11719922—42no—
103C2×#11719922C2314yes—
104C2×#11719917—42no—
105C2×#11719917C2314yescomplemented
106C2×#11719912—42no—
107C2×#11719912C2314yes—
108C22×#88322C2311yescharacteristic
109C22×#88322C2311yescharacteristic
110#13133212—28no—
111#13133208—22no—
112#13133208C2314yescomplemented
113#13133204—22no—
114#13133204C2314yes—
115#13133202—28no—
116#13133199—28no—
117#13133197—22no—
118#13133197C2314yes—
119#13133192—22no—
120#13133192C2314yes—
121#13133191—22no—
122#13133191—28no—
123#13133191C2314yescomplemented
124#13133188—28no—
125#13133185—28no—
126#13133179—22no—
127#13133179—22no—
128#13133179C2314yes—
129#13133179C2314yescomplemented
130C4×C22⋊D53—28no—
131C4×C22⋊D53D414yes—
132C4×C22⋊D53C2314yes—
133#13133175—22no—
134#13133175C2314yes—
135C2×C4⋊Dic53—21no—
136C2×C4⋊Dic53—21no—
137C2×C4⋊Dic53C2311yescharacteristic
138C2×#11719919—21no—
139C2×#11719919D411yescharacteristic
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53D411yescharacteristic
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921D411yescharacteristic
150C22⋊C4×D53—28no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53C2311yescharacteristic
153#13133148C2314yescomplemented
154#13133146C2314yescomplemented
155#13133142C2314yescomplemented
156#13133140C2314yescomplemented
157#13133140C2314yescomplemented
158#13133139C2314yes—
159#13133138C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162#13133137C2314yescomplemented
163#13133129C2314yes—
164C8×Dic53C2314yescomplemented
165C22×D4×C53—21no—
166C22×D4×C53C2311yescharacteristic
167C23×C4×C53—21no—
168C23×C4×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171#121×C53—22no—
172#121×C53C2314yes—
173C2×C4⋊C4×C53—22no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2314yescomplemented
179C2×C22⋊C4×C53—21no—
180#107×C53C2314yescomplemented
181#107×C53C2314yescomplemented
182#102×C53C2314yes—
183#102×C53C2314yes—
184C22⋊C8×C53C2314yescomplemented
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53—21no—
189C23×D53—24no—
190C23×D53—44no—
191C23×D53—44no—
192C23×D53—82no—
193C23×D53C2×D411yescharacteristic
194C2×D4×C53—24no—
195C2×D4×C53—21no—
196C2×D4×C53—22no—
197C2×D4×C53—22no—
198C2×D4×C53—82no—
199C2×D4×C53C2412yes—
200C22×C4×C53—22no—
201C22×C4×C53—22no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—24no—
206C22×C4×C53—82no—
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D412yes—
209C22×C4×C53C2412yes—
210C22×C4×C53C2411yescharacteristic
211C2×C22⋊D53—24no—
212C2×C22⋊D53—24no—
213C2×C22⋊D53—24no—
214C2×C22⋊D53—42no—
215C2×C22⋊D53—44no—
216C2×C22⋊D53—44no—
217C2×C22⋊D53—44no—
218C2×C22⋊D53C2×D414yes—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223C22×Dic53C2×D411yescharacteristic
224D4×D53—28no—
225D4×D53—44no—
226D4×D53—48no—
227#11719945—28no—
228#11719945—44no—
229#11719945—48no—
230C2×D212—21no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—22no—
234C2×D212—21no—
235C2×D212—24no—
236C2×D212—82no—
237C2×D212#4114yes—
238C2×D212C2412yes—
239C2×D212C2412yes—
240C2×C4×D53—22no—
241C2×C4×D53—22no—
242C2×C4×D53—24no—
243C2×C4×D53—24no—
244C2×C4×D53—24no—
245C2×C4×D53—44no—
246C2×C4×D53—82no—
247C2×C4×D53—82no—
248C2×C4×D53C2×D412yes—
249C2×C4×D53C2412yes—
250C2×Dic106—22no—
251C2×Dic106—22no—
252C2×Dic106—21no—
253C2×Dic106C2412yes—
254C2×C8×C53—22no—
255C2×C8×C53—22no—
256C2×C8×C53C2412yes—
257C2×C8×C53C2412yes—
258C4⋊C4×C53—21no—
259C4⋊C4×C53—21no—
260C4⋊C4×C53—24no—
261C4⋊C4×C53—21no—
262C4⋊C4×C53C2412yes—
263C4⋊C4×C53C2412yes—
264C4⋊C4×C53C2412yes—
265C22⋊C4×C53—24no—
266C22⋊Dic53—24no—
267C22⋊Dic53—24no—
268C22⋊Dic53C2×D414yes—
269#11719922—44no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921C2×D414yes—
277C4⋊Dic53—21no—
278C4⋊Dic53—24no—
279C4⋊Dic53—24no—
280C4⋊Dic53C2412yes—
281#11719919—24no—
282#11719919C2×D414yes—
283C4×Dic53—24no—
284C4×Dic53C2×D412yes—
285C4×Dic53C2412yes—
286#11719917—44no—
287C2×#88322—22no—
288C2×#88322—22no—
289C2×#88322C2412yes—
290C2×#88322C2412yes—
291D424—28no—
292#11719913—44no—
293#11719912—44no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—42no—
299C23×C53—42no—
300C23×C53—42no—
301C23×C53C22×D412yes—
302C23×C53C22×D411yescharacteristic
303C22×D53—22no—
304C22×D53—24no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—48no—
310C22×D53—48no—
311C22×D53—42no—
312C22×D53—42no—
313C22×D53—42no—
314C22×D53—42no—
315C22×D53—42no—
316C22×D53—84no—
317C22×D53—816no—
318C22×D53C22×D412yes—
319D4×C53—22no—
320D4×C53—22no—
321D4×C53—42no—
322D4×C53—84no—
323C2×C4×C53—22no—
324C2×C4×C53—24no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—42no—
331C2×C4×C53—42no—
332C2×C4×C53—42no—
333C2×C4×C53—84no—
334C2×C4×C53C22×D412yes—
335C2×C4×C53C22×D411yescharacteristic
336C2×C4×C53C2×#4112yes—
337C2×C4×C53H(5,𝔽2)12yes—
338C2×C4×C53C2511yescharacteristic
339C22⋊D53—44no—
340C22⋊D53—48no—
341C22⋊D53—48no—
342C22⋊D53—48no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—42no—
349C2×Dic53—42no—
350C2×Dic53C22×D412yes—
351C2×Dic53C22×D412yes—
352C2×Dic53C22×D412yes—
353D212—24no—
354D212—22no—
355D212—22no—
356D212—22no—
357D212—42no—
358D212—84no—
359D212C2×#4114yes—
360C4×D53—24no—
361C4×D53—22no—
362C4×D53—22no—
363C4×D53—48no—
364C4×D53—84no—
365C4×D53—84no—
366Dic106—22no—
367Dic106—22no—
368Dic106—42no—
369C8×C53—22no—
370C8×C53—22no—
371#88322—22no—
372#88322—22no—
373C2×#3322—531nomaximal, Sylow
374C22×C53—22no—
375C22×C53—22no—
376C22×C53—22no—
377C22×C53—44no—
378C22×C53—42no—
379C22×C53—42no—
380C22×C53—42no—
381C22×C53—84no—
382C22×C53#54612yes—
383C22×C53#57512yes—
384C22×C53#57612yes—
385C22×C53C23×D411yescharacteristic
386C2×D53—22no—
387C2×D53—24no—
388C2×D53—22no—
389C2×D53—22no—
390C2×D53—44no—
391C2×D53—48no—
392C2×D53—42no—
393C2×D53—42no—
394C2×D53—42no—
395C2×D53—42no—
396C2×D53—42no—
397C2×D53—816no—
398C2×D53—84no—
399C4×C53—22no—
400C4×C53—42no—
401C4×C53—42no—
402C4×C53—42no—
403C4×C53#54612yes—
404C4×C53C22×#4111yescharacteristic
405C4×C53C2×H(5,𝔽2)11yescharacteristic
406Dic53—22no—
407Dic53—22no—
408Dic53—22no—
409Dic53—42no—
410Dic53—42no—
411C2×#553—531no—
412C2×#546—531no—
413#3322—5316no—
414C2×#488—531no—
415C2×#485—531no—
416C2×#480D5311yescharacteristic, complemented
417C2×#478—531no—
418C2×#469—531no—
419C2×#468—531no—
420C2×#463—531no—
421C2×#449—531no—
422C2×#447—531no—
423C2×C4×D8—531no—
424C2×#436—531no—
425C2×#417—531no—
426C2×#418—531no—
427C2×C53—42no—
428C2×C53—82no—
429C2×C53#332214yescomplemented
430C2×C53C2×#54611yescharacteristic
431C2×C53C2×#57511yescharacteristic
432C2×C53C2×#57611yescharacteristic
433D53—42no—
434D53—44no—
435D53—82no—
436C22×#41—531no—
437C23×D4—531no—
438C22×SD16—531no—
439C22×D8—531no—
440C22×D8—531no—
441C22×M16—531no—
442C22×M16—531no—
443#553—538no—
444#553—1064no—
445#546—538no—
446#546—1064no—
447C2×#126—1061no—
448C2×#125—531no—
449C2×#124—531no—
450C2×#123—1061no—
451C2×#123—1061no—
452C2×C22⋊Q8—531no—
453C2×#121—531no—
454C2×#121—531no—
455C2×#121—1061no—
456C2×#121—1061no—
457C2×#121C2×D5311yescharacteristic
458C2×#120—1061no—
459C2×C4×D4—531no—
460C2×C4×D4—531no—
461C2×C4×D4—531no—
462C2×C4×D4—1061no—
463C2×#117—531no—
464C22×C4⋊C4C2×D5311yescharacteristic, complemented
465C22×C22⋊C4—1061no—
466#488—538no—
467#485—538no—
468#480C2×D5318yescomplemented
469#478—538no—
470#469—538no—
471#468—538no—
472#463—538no—
473#449—538no—
474#447—538no—
475C4×D8—538no—
476#436—538no—
477C2×#107C2×D5311yescharacteristic, complemented
478C2×#107C2×D5311yescharacteristic, complemented
479C2×#106—531no—
480C2×C4⋊C8—531no—
481#418—538no—
482#417—538no—
483C2×#103—531no—
484C2×#103—531no—
485C2×#103—531no—
486C2×#102—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×#102—531no—
490C2×#102—531no—
491C2×#102C2×D5311yescharacteristic
492C2×#102C2×D5311yescharacteristic
493C2×C22⋊C8—531no—
494C2×C22⋊C8C2×D5311yescharacteristic, complemented
495C2×C4×C8—531no—
496C53C2×#332211yescharacteristic, complemented, Sylow
497C25—1061no—
498C2×#41—534no—
499C2×#41—1064no—
500C2×#41—1062no—
501C2×#41—2122no—
502C22×Q8—531no—
503C22×D4—21no—
504C22×D4—531no—
505C22×D4—534no—
506C22×D4—531no—
507C22×D4—531no—
508C22×D4—1061no—
509C22×D4—1062no—
510C22×D4—1061no—
511C22×D4—1064no—
512C22×D4—1061no—
513C22×D4—1061no—
514C22×D4—2122no—
515C22×D4C22×D5311yescharacteristic
516C23×C4—21no—
517C23×C4—531no—
518C23×C4—1061no—
519C23×C4—1061no—
520C23×C4—1061no—
521C23×C4C22×D5311yescharacteristic
522C2×SD16—534no—
523C2×SD16—2122no—
524C2×D8—534no—
525C2×D8—534no—
526C2×D8—1064no—
527C2×D8—2122no—
528C2×M16—534no—
529C2×M16—534no—
530C2×M16—2122no—
531C2×M16—2122no—
532C22×C8—531no—
533C22×C8—531no—
534C22×C8C22×D5311yescharacteristic
535C22×C8C22×D5311yescharacteristic
536#126—1068no—
537#125—534no—
538#125—1062no—
539#124—534no—
540#124—1062no—
541#123—1068no—
542#123—1068no—
543C22⋊Q8—534no—
544C22⋊Q8—1062no—
545#121—22no—
546#121—534no—
547#121—534no—
548#121—1068no—
549#121—1062no—
550#121—1068no—
551#121—1062no—
552#121C22×D5314yes—
553#120—1068no—
554C4×D4—534no—
555C4×D4—534no—
556C4×D4—534no—
557C4×D4—534no—
558C4×D4—1062no—
559C4×D4—1062no—
560C4×D4—1068no—
561#117—534no—
562#117—1062no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—531no—
566C2×C4⋊C4—531no—
567C2×C4⋊C4—1061no—
568C2×C4⋊C4—1061no—
569C2×C4⋊C4—1061no—
570C2×C4⋊C4C22×D5311yescharacteristic
571C2×C4⋊C4C22×D5311yescharacteristic
572C2×C4⋊C4C22×D5311yescharacteristic
573C2×C4⋊C4C22×D5314yescomplemented
574C2×C22⋊C4—21no—
575C2×C22⋊C4—531no—
576C2×C22⋊C4—531no—
577C2×C22⋊C4—1068no—
578C2×C22⋊C4—1061no—
579C2×C22⋊C4—1061no—
580C2×C22⋊C4—1061no—
581C2×C22⋊C4—1061no—
582C2×C22⋊C4—1061no—
583C2×C22⋊C4—1061no—
584C2×C22⋊C4—1061no—
585C2×C22⋊C4—1061no—
586C2×C42—531no—
587C2×C42—1061no—
588#107C22×D5314yescomplemented
589#107C22×D5314yescomplemented
590#106—534no—
591C4⋊C8—534no—
592#103—534no—
593#103—534no—
594#103—534no—
595#102—534no—
596#102—534no—
597#102—534no—
598#102—534no—
599#102—534no—
600#102C22×D5314yes—
601#102C22×D5314yes—
602C22⋊C8—534no—
603C22⋊C8C22×D5314yescomplemented
604C4×C8—534no—
605C24—21no—
606C24—531no—
607C24—1064no—
608C24—1061no—
609C24—1061no—
610C24—4242no—
611C24—2124no—
612C24—2124no—
613C24D4×D5311yescharacteristic
614#41—1068no—
615#41—2124no—
616#41—2128no—
617C2×Q8—532no—
618C2×Q8—1061no—
619C2×Q8—1062no—
620C2×Q8—1062no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—82no—
626C2×D4—534no—
627C2×D4—534no—
628C2×D4—532no—
629C2×D4—532no—
630C2×D4—1064no—
631C2×D4—1064no—
632C2×D4—1068no—
633C2×D4—1064no—
634C2×D4—1064no—
635C2×D4—1061no—
636C2×D4—1061no—
637C2×D4—1062no—
638C2×D4—1062no—
639C2×D4—1062no—
640C2×D4—4242no—
641C2×D4—2124no—
642C2×D4—2128no—
643C2×D4—2122no—
644C2×D4—2124no—
645C2×D4—2124no—
646C2×D4—2124no—
647C2×D4C23×D5312yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—82no—
655C22×C4—531no—
656C22×C4—531no—
657C22×C4—531no—
658C22×C4—532no—
659C22×C4—532no—
660C22×C4—1064no—
661C22×C4—1064no—
662C22×C4—1062no—
663C22×C4—1062no—
664C22×C4—1061no—
665C22×C4—1061no—
666C22×C4—1064no—
667C22×C4—4242no—
668C22×C4—4242no—
669C22×C4—2124no—
670C22×C4D4×D5312yes—
671C22×C4D4×D5311yescharacteristic
672C22×C4C23×D5312yes—
673C22×C4C23×D5311yescharacteristic
674SD16—2124no—
675D8—1068no—
676D8—2124no—
677M16—2124no—
678M16—2124no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—532no—
682C2×C8—532no—
683C2×C8—1062no—
684C2×C8—1062no—
685C2×C8C23×D5312yes—
686C2×C8C23×D5312yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—24no—
690C4⋊C4—21no—
691C4⋊C4—534no—
692C4⋊C4—532no—
693C4⋊C4—1064no—
694C4⋊C4—1064no—
695C4⋊C4—1064no—
696C4⋊C4—1061no—
697C4⋊C4C23×D5312yes—
698C4⋊C4C23×D5312yes—
699C4⋊C4C23×D5312yes—
700C22⋊C4—24no—
701C22⋊C4—534no—
702C22⋊C4—534no—
703C22⋊C4—1064no—
704C22⋊C4—1064no—
705C22⋊C4—1064no—
706C22⋊C4—1064no—
707C22⋊C4—1064no—
708C22⋊C4—1064no—
709C22⋊C4—1064no—
710C22⋊C4—1064no—
711C42—532no—
712C42—532no—
713C42—1064no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—532no—
722C23—1062no—
723C23—1064no—
724C23—1062no—
725C23—1062no—
726C23—1062no—
727C23—1062no—
728C23—4244no—
729C23—42416no—
730C23—2128no—
731C23—2128no—
732C23—2122no—
733C23—2122no—
734C23—2122no—
735C23—2122no—
736C23—2122no—
737C23C2×D4×D5312yes—
738C23C2×D4×D5311yescharacteristic
739Q8—1062no—
740Q8—1062no—
741Q8—2122no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—84no—
746D4—534no—
747D4—1064no—
748D4—1062no—
749D4—1062no—
750D4—1062no—
751D4—4244no—
752D4—2124no—
753D4—2128no—
754D4—2128no—
755D4—2128no—
756D4—2122no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—84no—
768C2×C4—532no—
769C2×C4—532no—
770C2×C4—532no—
771C2×C4—1062no—
772C2×C4—1062no—
773C2×C4—1062no—
774C2×C4—1064no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—1062no—
778C2×C4—1062no—
779C2×C4—4244no—
780C2×C4—4244no—
781C2×C4—2128no—
782C2×C4—2122no—
783C2×C4—2122no—
784C2×C4C2×D4×D5312yes—
785C2×C4C2×D4×D5311yescharacteristic
786C2×C4#41×D5312yes—
787C2×C4#1313326312yes—
788C2×C4C24×D5311yescharacteristic
789C8—22no—
790C8—22no—
791C8—1062no—
792C8—1062no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—1062no—
802C22—1064no—
803C22—1062no—
804C22—1062no—
805C22—42416no—
806C22—4244no—
807C22—2122no—
808C22—2122no—
809C22—2122no—
810C22—2122no—
811C22—2122no—
812C22—2124no—
813C22—2128no—
814C22#1681126512yes—
815C22#1681142212yes—
816C22#1681142412yes—
817C22C22×D4×D5311yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—1062no—
823C4—1062no—
824C4—1062no—
825C4—2122no—
826C4—2122no—
827C4#1681126512yes—
828C4C2×#41×D5311yescharacteristic
829C4C2×#1313326311yescharacteristic
830C2—42no—
831C2—82no—
832C2—4242no—
833C2—2122no—
834C2—2124no—
835C2#2028691914yesdirect product factor
836C2C2×#1681126511yescharacteristic
837C2C2×#1681142211yescharacteristic
838C2C2×#1681142411yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#480C2
socleC23×C53C22×D4
hypercenterC2×#480D53
hypocenterC53C2×#3322
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#16811321C2semidirect
2. C2×#16811270C2semidirect
3. #20286919C2direct (N × H)
4. C2×#16810976C2semidirect
5. C2×#16810966C2semidirect
6. C2×#16810926C2semidirect
7. C2×#16810874C2semidirect
8. C2×#16810870C2semidirect
9. C2×#16810837C2semidirect
10. C2×#16810770C2semidirect
11. C2×#16810758C2semidirect
12. C2×#16810705C2semidirect
13. C2×#16810698C2semidirect
14. C2×#16810622C2semidirect
15. C2×#16810626C2semidirect
16. C2×C53×#480C2semidirect
19. C22×#11719913C22semidirect
22. C22×#11719917C22semidirect
25. #16811321C22semidirect
27. #16811270C22semidirect
29. C2×#13133208C22semidirect
36. C2×#13133191C22semidirect
40. C2×#13133179C22semidirect
45. #16810976C22semidirect
46. #16810966C22semidirect
47. #16810926C22semidirect
48. #16810874C22semidirect
49. #16810870C22semidirect
50. #16810837C22semidirect
51. #16810770C22semidirect
52. #16810758C22semidirect
53. #16810705C22semidirect
54. #16810698C22semidirect
55. C2×#13133148C22semidirect
56. C2×#13133146C22semidirect
57. #16810626C22semidirect
58. #16810622C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133140C22semidirect
61. C2×#13133140C22semidirect
66. C2×#13133137C22semidirect
68. C2×C8×Dic53C22semidirect
70. C22×C4⋊C4×C53C22semidirect
71. C53×#480C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#107×C53C22semidirect
76. C2×C22⋊C8×C53C22semidirect
99. C2×#11719913C23semidirect
105. C2×#11719917C23semidirect
112. #13133208C23semidirect
123. #13133191C23semidirect
129. #13133179C23semidirect
153. #13133148C23semidirect
154. #13133146C23semidirect
155. #13133142C23semidirect
156. #13133140C23semidirect
157. #13133140C23semidirect
162. #13133137C23semidirect
164. C8×Dic53C23semidirect
178. C2×C4⋊C4×C53C23semidirect
180. #107×C53C23semidirect
181. #107×C53C23semidirect
184. C22⋊C8×C53C23semidirect
416. C2×#480D53semidirect
429. C2×C53#3322semidirect
464. C22×C4⋊C4C2×D53semidirect
468. #480C2×D53semidirect
477. C2×#107C2×D53semidirect
478. C2×#107C2×D53semidirect
494. C2×C22⋊C8C2×D53semidirect
496. C53C2×#3322semidirect
573. C2×C4⋊C4C22×D53semidirect
588. #107C22×D53semidirect
589. #107C22×D53semidirect
603. C22⋊C8C22×D53semidirect
835. C2#20286919direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113212
C2×#168112702
#202869192
C2×#168109762
C2×#168109662
C2×#168109262
C2×#168108742
C2×#168108702
C2×#168108372
C2×#168107702
C2×#168107582
C2×#168107052
C2×#168106982
C2×#168106222
C2×#168106262
C2×C53×#4802
C2×#332253