Finite Group Databasebeta

← C2×#20286867 #28260774

Subgroups — C2×#20286867 #28260774

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×#16811336C211yesmaximal, characteristic, complemented
2C2×#16811261C211yesmaximal, characteristic, complemented
3#20286867C2116yesmaximal, direct product factor
4C2×#16810984C211yesmaximal, characteristic, complemented
5C2×#16810963C211yesmaximal, characteristic, complemented
6C2×#16810947C211yesmaximal, characteristic, complemented
7C2×#16810901C211yesmaximal, characteristic, complemented
8C2×#16810872C211yesmaximal, characteristic, complemented
9C2×#16810859C211yesmaximal, characteristic, complemented
10C2×#16810841C211yesmaximal, characteristic, complemented
11C2×#16810768C211yesmaximal, characteristic, complemented
12C2×#16810758C211yesmaximal, characteristic, complemented
13C2×#16810732C211yesmaximal, characteristic, complemented
14C2×#16810694C211yesmaximal, characteristic, complemented
15C2×#16810626C211yesmaximal, characteristic, complemented
16C2×C53×#416C211yesmaximal, characteristic, complemented
17C22×D4×D53C2211yescharacteristic
18C22×#11719924C2211yescharacteristic, complemented
19C22×D424C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22#16811336—24no—
23#16811336C2218yescomplemented
24#16811261—24no—
25#16811261C2218yescomplemented
26C2×#13133216C2211yescharacteristic, complemented
27C2×#13133206C2211yescharacteristic
28C2×#13133205—21no—
29C2×#13133203—21no—
30C2×#13133200—21no—
31C2×#13133193C2211yescharacteristic
32C2×#13133192C2211yescharacteristic
33C2×#13133191C2211yescharacteristic
34C2×#13133191C2211yescharacteristic, complemented
35C2×#13133190—21no—
36C2×#13133189—21no—
37C2×#13133185—21no—
38C2×D4×Dic53C2211yescharacteristic
39C2×#13133179C2211yescharacteristic, complemented
40C2×C4×C22⋊D53C2211yescharacteristic
41C2×#13133175C2211yescharacteristic
42C2×#13133174—21no—
43C22×#11719921—21no—
44#16810984C2218yescomplemented
45#16810963C2218yescomplemented
46#16810947C2218yescomplemented
47#16810901C2218yescomplemented
48#16810872C2218yescomplemented
49#16810859C2218yescomplemented
50#16810841C2218yescomplemented
51#16810768C2218yescomplemented
52#16810758C2218yescomplemented
53#16810732C2218yescomplemented
54#16810694C2218yescomplemented
55C2×#13133151C2211yescharacteristic, complemented
56C2×#13133150C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×#13133146C2211yescharacteristic, complemented
59#16810626C2218yescomplemented
60C2×#13133141C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic, complemented
63C2×#13133138C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic, complemented
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic, complemented
69C22×#41×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic, complemented
71C2×#117×C53C2211yescharacteristic, complemented
72C53×#416C2218yescomplemented
73C2×#103×C53C2211yescharacteristic, complemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C24×D53—21no—
78C22×Dic106—21no—
79C22×D212—21no—
80C22×D212C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C22×C22⋊D53D411yescharacteristic
86C2×D4×D53—24no—
87C2×D4×D53—22no—
88C2×D4×D53—42no—
89C2×D4×D53C2314yes—
90C23×Dic53—21no—
91C22×C4×D53—21no—
92C22×C4×D53C2311yescharacteristic
93C2×#11719924—42no—
94C2×#11719924C2314yescomplemented
95C2×D424—42no—
96C2×D424C2314yes—
97C2×#11719922—24no—
98C2×#11719922C2314yes—
99C2×#11719912—42no—
100C2×#11719912C2314yes—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103#13133216—22no—
104#13133216C2314yescomplemented
105#13133206—22no—
106#13133206C2314yes—
107#13133205—28no—
108#13133203—28no—
109#13133200—28no—
110#13133193—22no—
111#13133193C2314yes—
112#13133192—22no—
113#13133192C2314yes—
114#13133191—22no—
115#13133191—22no—
116#13133191C2314yes—
117#13133191C2314yescomplemented
118#13133190—28no—
119#13133189—28no—
120#13133185—28no—
121D4×Dic53—22no—
122D4×Dic53C2314yes—
123#13133179—22no—
124#13133179C2314yescomplemented
125C4×C22⋊D53D414yes—
126C4×C22⋊D53C2314yes—
127#13133175—22no—
128#13133175C2314yes—
129#13133174—28no—
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919D411yescharacteristic
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53D411yescharacteristic
137C2×#11719921—28no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921D411yescharacteristic
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133151C2314yescomplemented
150#13133150C2314yescomplemented
151#13133148C2314yescomplemented
152#13133146C2314yescomplemented
153#13133141C2314yescomplemented
154#13133139C2314yes—
155#13133139C2314yescomplemented
156#13133138C2314yes—
157#13133137C2314yes—
158#13133137C2314yes—
159C22⋊#88322C2314yescomplemented
160#13133129C2314yes—
161#13133127C2314yescomplemented
162C2×#41×C53—22no—
163C2×#41×C53—24no—
164C2×#41×C53—42no—
165C2×#41×C53C2314yes—
166C22×Q8×C53C2311yescharacteristic
167C22×D4×C53—21no—
168C22×D4×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C23×C4×C53C2311yescharacteristic
171C22×C8×C53—42no—
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2314yescomplemented
175#117×C53—22no—
176#117×C53C2314yescomplemented
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C22⋊C4×C53—21no—
180C2×C42×C53—21no—
181#103×C53C2314yescomplemented
182#103×C53C2314yescomplemented
183#102×C53C2314yes—
184#102×C53C2314yes—
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
194#41×C53—28no—
195#41×C53—44no—
196#41×C53—48no—
197C2×Q8×C53—21no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53C2412yes—
201C2×D4×C53—24no—
202C2×D4×C53—21no—
203C2×D4×C53—22no—
204C2×D4×C53—44no—
205C2×D4×C53#4114yes—
206C2×D4×C53C2412yes—
207C22×C4×C53—22no—
208C22×C4×C53—22no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—24no—
213C22×C4×C53—44no—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2412yes—
217C22×C4×C53C2411yescharacteristic
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—42no—
222C2×C22⋊D53—44no—
223C2×C22⋊D53—82no—
224C2×C22⋊D53—82no—
225C2×C22⋊D53C2×D414yes—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—24no—
229C22×Dic53—82no—
230C22×Dic53C2×D411yescharacteristic
231C22×Dic53C2×D411yescharacteristic
232C22×Dic53C2×D411yescharacteristic
233D4×D53—28no—
234D4×D53—44no—
235D4×D53—48no—
236C2×D212—22no—
237C2×D212—22no—
238C2×D212—22no—
239C2×D212—22no—
240C2×D212—21no—
241C2×D212—21no—
242C2×D212—24no—
243C2×D212—82no—
244C2×D212C2412yes—
245C2×D212C2412yes—
246C2×C4×D53—22no—
247C2×C4×D53—22no—
248C2×C4×D53—24no—
249C2×C4×D53—44no—
250C2×C4×D53C2×D412yes—
251C2×C4×D53C2412yes—
252C2×Dic106—24no—
253C2×Dic106—82no—
254C2×C8×C53—22no—
255C2×C8×C53—22no—
256C2×C8×C53—44no—
257C2×C8×C53C2412yes—
258C2×C8×C53C2412yes—
259C4⋊C4×C53—21no—
260C4⋊C4×C53—21no—
261C4⋊C4×C53C2412yes—
262C4⋊C4×C53C2412yes—
263C22⋊C4×C53—24no—
264C42×C53—24no—
265C22⋊Dic53—24no—
266C22⋊Dic53C2×D414yes—
267#11719924—44no—
268#11719922—28no—
269#11719921—24no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921—24no—
277#11719921C2×D414yes—
278C4⋊Dic53—21no—
279C4⋊Dic53—21no—
280C4⋊Dic53C2412yes—
281C4⋊Dic53C2412yes—
282#11719919—24no—
283#11719919—24no—
284#11719919C2×D414yes—
285C4×Dic53—24no—
286C4×Dic53C2×D412yes—
287C4×Dic53C2412yes—
288C2×#88322—22no—
289C2×#88322—22no—
290C2×#88322C2412yes—
291C2×#88322C2412yes—
292D424—44no—
293#11719912—44no—
294C23×C53—24no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—42no—
300C23×C53—42no—
301C23×C53C22×D412yes—
302C23×C53C22×D411yescharacteristic
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—48no—
309C22×D53—48no—
310C22×D53—42no—
311C22×D53—42no—
312C22×D53—42no—
313C22×D53—42no—
314C22×D53—42no—
315C22×D53—42no—
316C22×D53—84no—
317C22×D53—816no—
318C22×D53C22×D412yes—
319Q8×C53—22no—
320Q8×C53—22no—
321Q8×C53—42no—
322D4×C53—24no—
323D4×C53—22no—
324D4×C53—48no—
325D4×C53C2×#4114yes—
326C2×C4×C53—22no—
327C2×C4×C53—24no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—48no—
334C2×C4×C53—42no—
335C2×C4×C53—42no—
336C2×C4×C53—42no—
337C2×C4×C53C22×D412yes—
338C2×C4×C53C22×D411yescharacteristic
339C2×C4×C53C2×#4112yes—
340C2×C4×C53H(5,𝔽2)12yes—
341C2×C4×C53C2511yescharacteristic
342C22⋊D53—44no—
343C22⋊D53—48no—
344C22⋊D53—84no—
345C22⋊D53—84no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—22no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—42no—
352C2×Dic53—42no—
353C2×Dic53—84no—
354C2×Dic53C22×D412yes—
355C2×Dic53C22×D412yes—
356C2×Dic53C22×D412yes—
357D212—22no—
358D212—22no—
359D212—22no—
360D212—22no—
361D212—42no—
362D212—42no—
363D212—84no—
364C4×D53—24no—
365C4×D53—22no—
366C4×D53—22no—
367C4×D53—48no—
368Dic106—84no—
369C8×C53—22no—
370C8×C53—22no—
371#88322—22no—
372#88322—22no—
373C2×#3319—531nomaximal, Sylow
374C22×C53—24no—
375C22×C53—22no—
376C22×C53—22no—
377C22×C53—22no—
378C22×C53—48no—
379C22×C53—44no—
380C22×C53—42no—
381C22×C53—42no—
382C22×C53#54612yes—
383C22×C53#57512yes—
384C22×C53#57612yes—
385C22×C53C23×D411yescharacteristic
386C2×D53—22no—
387C2×D53—22no—
388C2×D53—22no—
389C2×D53—44no—
390C2×D53—42no—
391C2×D53—42no—
392C2×D53—42no—
393C2×D53—42no—
394C2×D53—42no—
395C2×D53—42no—
396C2×D53—816no—
397C2×D53—84no—
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×#555—531no—
412C2×#546—531no—
413#3319—5316no—
414C2×#489—531no—
415C2×#485—531no—
416C2×#482—531no—
417C2×#474—531no—
418C2×#468—531no—
419C2×#466—531no—
420C2×#463—531no—
421C2×#449—531no—
422C2×#447—531no—
423C2×#442—531no—
424C2×#435—531no—
425C2×#418—531no—
426C2×#416D5311yescharacteristic, complemented
427C2×C53—44no—
428C2×C53—42no—
429C2×C53#331914yescomplemented
430C2×C53C2×#54611yescharacteristic
431C2×C53C2×#57511yescharacteristic
432C2×C53C2×#57611yescharacteristic
433D53—42no—
434D53—82no—
435D53—82no—
436C22×#41C2×D5311yescharacteristic
437C23×D4—531no—
438C22×SD16—531no—
439C22×D8—531no—
440C22×D8—531no—
441C22×M16—531no—
442C23×C8C2×D5311yescharacteristic, complemented
443#555—538no—
444#555—1064no—
445#546—538no—
446#546—1064no—
447C2×C4⋊Q8—531no—
448C2×#124—531no—
449C2×#124—1061no—
450C2×#124—1061no—
451C2×#123—1061no—
452C2×C22⋊Q8—531no—
453C2×#121—531no—
454C2×#121—531no—
455C2×#121—531no—
456C2×#121—1061no—
457C2×#121—1061no—
458C2×#120—1061no—
459C2×C4×D4—531no—
460C2×C4×D4—531no—
461C2×C4×D4—531no—
462C2×#117—531no—
463C2×#117—1061no—
464C2×#117C2×D5311yescharacteristic, complemented
465C22×C22⋊C4—1061no—
466#489—538no—
467#485—538no—
468#482—538no—
469#474—538no—
470#468—538no—
471#466—538no—
472#463—538no—
473#449—538no—
474#447—538no—
475#442—538no—
476#435—538no—
477C2×#107—531no—
478C2×#107—531no—
479C2×#106—531no—
480C2×C4⋊C8—531no—
481#418—538no—
482#416C2×D5318yescomplemented
483C2×#103—531no—
484C2×#103C2×D5311yescharacteristic, complemented
485C2×#103C2×D5311yescharacteristic, complemented
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⋊C8—531no—
495C2×#97—531no—
496C53C2×#331911yescharacteristic, complemented, Sylow
497C25—1061no—
498C2×#41—22no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41C22×D5314yes—
502C22×Q8—1061no—
503C22×Q8C22×D5311yescharacteristic
504C22×D4—21no—
505C22×D4—531no—
506C22×D4—534no—
507C22×D4—531no—
508C22×D4—531no—
509C22×D4—1061no—
510C22×D4—1062no—
511C22×D4—1061no—
512C22×D4—1064no—
513C22×D4—1061no—
514C22×D4—1061no—
515C22×D4—2122no—
516C22×D4C22×D5311yescharacteristic
517C23×C4—21no—
518C23×C4—531no—
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—2122no—
530C22×C8—42no—
531C22×C8—531no—
532C22×C8—531no—
533C22×C8C22×D5311yescharacteristic
534C22×C8C22×D5311yescharacteristic
535C22×C8C22×D5314yescomplemented
536C4⋊Q8—534no—
537C4⋊Q8—1062no—
538#124—534no—
539#124—1068no—
540#124—1062no—
541#124—1068no—
542#123—1068no—
543C22⋊Q8—534no—
544C22⋊Q8—1062no—
545#121—534no—
546#121—534no—
547#121—534no—
548#121—1068no—
549#121—1068no—
550#121—1062no—
551#121—1062no—
552#121—1062no—
553#120—1068no—
554C4×D4—534no—
555C4×D4—534no—
556C4×D4—534no—
557C4×D4—534no—
558C4×D4—1062no—
559C4×D4—1062no—
560#117—22no—
561#117—534no—
562#117—1068no—
563#117—1062no—
564#117C22×D5314yescomplemented
565C2×C4⋊C4—531no—
566C2×C4⋊C4—531no—
567C2×C4⋊C4—531no—
568C2×C4⋊C4—1061no—
569C2×C4⋊C4—1061no—
570C2×C4⋊C4C22×D5311yescharacteristic
571C2×C4⋊C4C22×D5311yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—531no—
574C2×C22⋊C4—531no—
575C2×C22⋊C4—1068no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
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×C42—21no—
586C2×C42—531no—
587C2×C42—1061no—
588#107—534no—
589#107—534no—
590#106—534no—
591C4⋊C8—534no—
592#103—534no—
593#103C22×D5314yescomplemented
594#103C22×D5314yescomplemented
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⋊C8—534no—
604#97—534no—
605C24—21no—
606C24—531no—
607C24—1064no—
608C24—1061no—
609C24—1061no—
610C24—4242no—
611C24—2124no—
612C24—2124no—
613C24D4×D5311yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—1064no—
621C2×Q8—4242no—
622C2×Q8C23×D5312yes—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—44no—
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—1062no—
641C2×D4—4242no—
642C2×D4—4242no—
643C2×D4—4242no—
644C2×D4—2124no—
645C2×D4—2128no—
646C2×D4—2122no—
647C2×D4—2124no—
648C2×D4#1171994514yes—
649C2×D4C23×D5312yes—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—44no—
657C22×C4—531no—
658C22×C4—531no—
659C22×C4—531no—
660C22×C4—532no—
661C22×C4—532no—
662C22×C4—1064no—
663C22×C4—1064no—
664C22×C4—1062no—
665C22×C4—1062no—
666C22×C4—1061no—
667C22×C4—1061no—
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—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—44no—
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—534no—
690C4⋊C4—532no—
691C4⋊C4—532no—
692C4⋊C4—1064no—
693C4⋊C4—1064no—
694C4⋊C4—1061no—
695C4⋊C4—1061no—
696C4⋊C4C23×D5312yes—
697C4⋊C4C23×D5312yes—
698C22⋊C4—24no—
699C22⋊C4—534no—
700C22⋊C4—534no—
701C22⋊C4—1064no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C22⋊C4—1064no—
705C22⋊C4—1064no—
706C22⋊C4—1064no—
707C22⋊C4—1064no—
708C22⋊C4—1064no—
709C22⋊C4—1064no—
710C42—24no—
711C42—532no—
712C42—532no—
713C42—1064no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—42no—
720C23—42no—
721C23—532no—
722C23—1062no—
723C23—1062no—
724C23—1062no—
725C23—1062no—
726C23—1062no—
727C23—4244no—
728C23—42416no—
729C23—2128no—
730C23—2128no—
731C23—2122no—
732C23—2122no—
733C23—2122no—
734C23—2122no—
735C23—2122no—
736C23—2122no—
737C23C2×D4×D5312yes—
738C23C2×D4×D5311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742Q8—4244no—
743D4—22no—
744D4—24no—
745D4—48no—
746D4—1062no—
747D4—1062no—
748D4—1062no—
749D4—1062no—
750D4—4244no—
751D4—4244no—
752D4—4244no—
753D4—2124no—
754D4—2128no—
755D4—2122no—
756D4—2122no—
757D4C2×#1171994514yes—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—48no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—532no—
770C2×C4—532no—
771C2×C4—532no—
772C2×C4—1062no—
773C2×C4—1062no—
774C2×C4—1062no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—1064no—
778C2×C4—1062no—
779C2×C4—1062no—
780C2×C4—4244no—
781C2×C4—2128no—
782C2×C4—2122no—
783C2×C4—2122no—
784C2×C4C2×D4×D5312yes—
785C2×C4C2×D4×D5311yescharacteristic
786C2×C4C2×#1171994512yes—
787C2×C4#1313326212yes—
788C2×C4C24×D5311yescharacteristic
789C8—22no—
790C8—22no—
791C8—1062no—
792C8—1062no—
793C22—22no—
794C22—24no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—48no—
799C22—42no—
800C22—42no—
801C22—1062no—
802C22—1062no—
803C22—1062no—
804C22—42416no—
805C22—4244no—
806C22—4244no—
807C22—2122no—
808C22—2122no—
809C22—2122no—
810C22—2122no—
811C22—2122no—
812C22—2122no—
813C22—2124no—
814C22#1681126312yes—
815C22#1681142012yes—
816C22#1681142512yes—
817C22C22×D4×D5311yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—1062no—
823C4—1062no—
824C4—1062no—
825C4—2122no—
826C4—2122no—
827C4#1681126312yes—
828C4C22×#1171994511yescharacteristic
829C4C2×#1313326211yescharacteristic
830C2—42no—
831C2—44no—
832C2—4242no—
833C2—4242no—
834C2—2122no—
835C2#2028686714yesdirect product factor
836C2C2×#1681126311yescharacteristic
837C2C2×#1681142011yescharacteristic
838C2C2×#1681142511yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#416C2
socleC23×C53C22×D4
hypercenterC2×#416D53
hypocenterC53C2×#3319
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#16811336C2semidirect
2. C2×#16811261C2semidirect
3. #20286867C2direct (N × H)
4. C2×#16810984C2semidirect
5. C2×#16810963C2semidirect
6. C2×#16810947C2semidirect
7. C2×#16810901C2semidirect
8. C2×#16810872C2semidirect
9. C2×#16810859C2semidirect
10. C2×#16810841C2semidirect
11. C2×#16810768C2semidirect
12. C2×#16810758C2semidirect
13. C2×#16810732C2semidirect
14. C2×#16810694C2semidirect
15. C2×#16810626C2semidirect
16. C2×C53×#416C2semidirect
18. C22×#11719924C22semidirect
23. #16811336C22semidirect
25. #16811261C22semidirect
26. C2×#13133216C22semidirect
34. C2×#13133191C22semidirect
39. C2×#13133179C22semidirect
44. #16810984C22semidirect
45. #16810963C22semidirect
46. #16810947C22semidirect
47. #16810901C22semidirect
48. #16810872C22semidirect
49. #16810859C22semidirect
50. #16810841C22semidirect
51. #16810768C22semidirect
52. #16810758C22semidirect
53. #16810732C22semidirect
54. #16810694C22semidirect
55. C2×#13133151C22semidirect
56. C2×#13133150C22semidirect
57. C2×#13133148C22semidirect
58. C2×#13133146C22semidirect
59. #16810626C22semidirect
60. C2×#13133141C22semidirect
62. C2×#13133139C22semidirect
66. C2×C22⋊#88322C22semidirect
68. C2×#13133127C22semidirect
70. C23×C8×C53C22semidirect
71. C2×#117×C53C22semidirect
72. C53×#416C22semidirect
73. C2×#103×C53C22semidirect
74. C2×#103×C53C22semidirect
94. C2×#11719924C23semidirect
104. #13133216C23semidirect
117. #13133191C23semidirect
124. #13133179C23semidirect
149. #13133151C23semidirect
150. #13133150C23semidirect
151. #13133148C23semidirect
152. #13133146C23semidirect
153. #13133141C23semidirect
155. #13133139C23semidirect
159. C22⋊#88322C23semidirect
161. #13133127C23semidirect
174. C22×C8×C53C23semidirect
176. #117×C53C23semidirect
181. #103×C53C23semidirect
182. #103×C53C23semidirect
426. C2×#416D53semidirect
429. C2×C53#3319semidirect
442. C23×C8C2×D53semidirect
464. C2×#117C2×D53semidirect
482. #416C2×D53semidirect
484. C2×#103C2×D53semidirect
485. C2×#103C2×D53semidirect
496. C53C2×#3319semidirect
535. C22×C8C22×D53semidirect
564. #117C22×D53semidirect
593. #103C22×D53semidirect
594. #103C22×D53semidirect
835. C2#20286867direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113362
C2×#168112612
#202868672
C2×#168109842
C2×#168109632
C2×#168109472
C2×#168109012
C2×#168108722
C2×#168108592
C2×#168108412
C2×#168107682
C2×#168107582
C2×#168107322
C2×#168106942
C2×#168106262
C2×C53×#4162
C2×#331953